1. Field of the Invention
The invention relates to a solidification analyzing method of analyzing solidification of molten alloy that can be used to conduct a die-casting simulation or the like, and to a solidification analyzing program for performing the solidification analyzing method.
2. Description of the Related Art
When parts made of aluminum (Al) alloy, magnesium (Mg) alloy, etc. are mass-produced, mold casting (die casting) is often used that is excellent in dimensional stability and by which a smooth casting surface is obtained. In the case of die casting, typically, a high pressure of approximately 20 to 80 MPa is applied to inject molten alloy into a cavity in a mold and the molten alloy is rapidly cooled to produce a casting.
However, even in the case of die casting, the solidification conditions of the molten alloy in the respective portions in the cavity vary depending on the path from the molten alloy supply position, the form of the cavity, etc., and a problem of occurrence of shrinkage cavity due to the solidification contraction can arise. Thus, conventionally, the optimum conditions were determined by repeating trial and error, such as changing the cooling conditions of the mold, in order to eliminate such a defect.
Such a method naturally needs high cost and the development efficiency is low. Thus, instead of trial and error using actual things, a method is becoming popular, in which with the use of computer simulation, the flow of the molten alloy and the solidification conditions during die casting are estimated in advance and, based on the obtained result, the search for the appropriate die casting conditions is efficiently conducted.
As such a method of analyzing solidification using simulation, an enthalpy method, an equivalent specific heat method, and a temperature recovery method, which are based on an equilibrium solidification model, and a local-equilibrium solidification model, in which local equilibrium between solid and liquid is assumed and solute distribution and segregation are taken into consideration, are frequently used. However, in such simulation based on (quasi)static model, the supercooling solidification phenomenon that occurs during actual casting is not taken into consideration and therefore, the analysis of temperature field and the solidification analysis are not always highly accurate. In particular, in the casting process, such as industrially important die casting, in which the cooling rate is high, the degree of supercooling is very high and it is necessary to take into consideration the supercooling solidification phenomenon in order to accurately predict the occurrence of casting defect.
A solidification analyzing method that takes into consideration the supercooling solidification phenomenon is described in Japanese Patent Application Publication No. 2003-33864 (JP-A-2003-33864) or “A Three-Dimensional Cellular Automaton-Finite Element Model for the Predication of Solidification Grain Structures”, Metallurgical and Materials Transaction A, Vol. 30, No. 12 (1999), p. 3153 (Non-Patent Document 1). Specifically, in these documents, there is a description concerning a method of analyzing solidification based on the nucleation/solidification-and-growth model with the use of the cellular automaton method. Specifically, the amount of nucleation in a nucleation model and the crystal growth rate in a solidification-and-growth model are treated as a function of the degree of supercooling and, focus is placed on the difference between the amount of emission of latent heat that is calculated based on the crystal growth rate and the amount of heat transferred to the surrounding area, whereby the supercooling solidification phenomenon is taken into consideration. However, the amount of nucleation when the solid nuclei are produced in the molten alloy is not the characteristic value concerning solidification that is accurately determined through experiment. Thus, in the case of the analyzing method in which the above-described cellular automaton method is used, the parameters related to the amount of nucleation are empirically given and therefore, it is difficult to incorporate the degree of supercooling during the supercooling solidification into the simulation with high accuracy. In addition, in the cellular automaton method, the time required to perform the analysis is very long and therefore, the cellular automaton method is not practical as the solidification analyzing method used for industrial products or utility articles.
In Japanese Patent Application Publication No. 5-96343 (JP-A-H05-96343), although not the die casting simulation, there is a description concerning a simulation of casting using cast iron. In this simulation, the supercooling solidification phenomenon is taken into consideration with the use of (i) the dependency of the number of graphite grains on cooling rate in a nucleation model and (ii) the speed of increase in the radii of graphite grains in a crystal growth model. In this case, because the number of graphite grains is the characteristic value concerning solidification that is experimentally determined with high reproducibility, it becomes possible to perform highly accurate solidification analysis with the supercooling solidification taken into consideration. However, the subject of this analysis is limited to the casting of nodular cast iron, the number of graphite grains in which can be measured, the Compacted Vermicular (CV) cast iron or the like that has a high glomeration rate and this simulation cannot be used for the die casting using Al alloy or Mg alloy that is employed for industrial use in many cases.
In “Influence of Degree of Supercooling on Solidification Characteristics in Solidification Analysis,” Foundry Engineering, Volume 78 (2006) No. 1 (Non-Patent Document 2), a solidification analyzing method obtained by adding the analysis of the amount of change in the fraction solid to the temperature recovery method, which is the equilibrium solidification analyzing method. Specifically, the supercooling solidification phenomenon is analyzed by appropriately estimating the amount of change in the fraction solid per unit time. However, in Non-Patent Document 2, the method of calculating the amount of increase in the fraction solid is treated as an issue, and it is difficult to match the experimental results and the analysis results. In addition, the method described in Non-Patent Document 2 does not reproduce the temperature recovery phenomenon (recalescence phenomenon) when the fraction solid is low, such as immediately after the start of solidification.